In-situ Observations of Lattice Parameter Fluctuations in ......S. S. Babu Formerly at Metals and...

METALLURGICAL & MATERIALS TRANSACTIONS A 36A (2005) 3281-3289

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In-situ Observations of Lattice Parameter Fluctuations inAustenite and Transformation to BainiteS. S. BabuFormerly at Metals and Ceramics Division, Oak Ridge National LaboratoryOak Ridge, TN 37831 USA, Currently at Edison Welding Institute, Columbus, Ohio43017, USAE. D. Specht and S. A. DavidMetals and Ceramics Division, Oak Ridge National LaboratoryOak Ridge, TN 37831 USAE. Karapetrova and P. ZschackFrederick Seitz Materials Research LaboratoryUniversity of Illinois at Urbana-ChampaignUrbana, Illinois 61801, USAM. Peet and H. K. D. H. BhadeshiaDepartment of Materials Science and MetallurgyUniversity of Cambridge, CB23QZUK

Corresponding Author: S. S. Babu, [email protected]; Tel: (614) 688-5206

Final version after the acceptance: Revised version after the comments from the reviewers ofMetallurgical and Materials Transactions 2005

The submitted manuscript has been authored by acontractor of the U.S. Government under contract DE-AC05-00OR22725. Accordingly, the U.S. Governmentretains a nonexclusive, royalty-free license to publish orreproduce the published form of this contribution, orallow others to do so, for U.S. Government purposes.


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AbstractThe isothermal transformation of high carbon austenite to bainitic ferrite has been investigatedwith the in situ technique of time-resolved X-ray diffraction using synchrotron radiation. Themeasurements indicate that prior to transformation, the austenite divided into regions withsignificantly different lattice parameters. It is possible that this is due to the development ofcarbon-rich and carbon-poor regions in the austenite, as a precursor to transformations includingthe bainite reaction. The lattice parameter became uniform as transformation progressed and thefraction of carbon-poor austenite decreased. The ferrite itself exhibited a large range of latticeparameters during the early stages of transformation, due to the trapping of carbon.

KeywordsSteels, Phase Transformations, Bainitic transformations, Time-resolved X-ray diffraction andTransformation Kinetics

IntroductionThe role of carbon during the transformation of austenite to bainitic ferrite in steels is interestingfrom a fundamental as well as a technological viewpoint. It is possible that bainite forms withoutdiffusion and carbon subsequently redistributes or precipitates as carbides [1,2]. An alternativeinterpretation is that the ferrite grows with its equilibrium carbon concentration [3,4]. Historically,it has also been speculated that the austenite becomes heterogeneous with carbon-enriched andcarbon-depleted regions, so that ferrite formation initiates in the carbon-depleted regions [5–11].In the present work, it has been possible to follow the lattice parameter changes associated withthe austenite at any temperature and during the course of the bainite transformation. If thechanges can be attributed to solute concentration then they help interpret the role of carbon.

ExperimentalThe chemical composition of the steels used in this investigation is Fe - 0.75C – 1.63Si –1.95Mn – 0.29Mo – 1.48Cr – 0.1V – 0.01Al – 0.003P – 0.003S wt%. This steel was selectedbecause, the transformation rate is slow due to high carbon concentration and there are no othertransformations including carbide precipitation that interfere with the formation of the bainiticferrite [12]. The microstructure following isothermal transformation is a mixture of bainitic ferriteand carbon-enriched retained austenite. The silicon concentration is sufficiently high to preventthe precipitation of cementite from the austenite, as would normally occur in the upper bainitetransformation temperature range [1].

Rectangular samples [2 × 4 × 95 mm] were made from this high-strength steel bar, which washomogenized at 1200°C for 48 hrs, for the diffraction experiments. It is important to note thatafter this homogenization treatment, the microstructure of the samples were essentiallymartensitic and with small amounts of retained austenite. Room temperature X-ray diffractionmeasurements also failed to show any texture in these samples. These homogenized sampleswere then heat-treated in-situ in a synchrotron beam line using resistive heating method.

The samples were heated to 1273 K and held at that temperature for 4 minutes. Then the steelwas cooled at a rate of 10 K s-1 from 1273 K to 573 K and held at that temperature for 12 hrs.The temperature was controlled using direct resistive-heating using a type S (Pt/Pt10%Rh)


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thermocouple. Oxidation was reduced by covering the sample with an inverted can filled withHe.

Bending magnet synchrotron radiation was provided by beam line X33-BM-B at the AdvancedPhoton Source (Argonne, Illinois). A double-crystal Si(111) monochromator selected andsagitally focused to 30 keV X rays. At this energy, the penetration depth in steel is 0.16 mm.Slits defined a beam 0.25 mm high and 1.0 mm wide on the sample. The incident beam wascarefully positioned well within the uniform temperature region of the sample. X rays wereincident on the sample surface at a glancing angle of 5°. A schematic illustration of theexperiment and a typical diffraction image is shown in Fig. 1. Diffracted X- rays were measuredusing a 1024x1024 pixel, Peltier-cooled, 16 bit CCD detector with a 60x60 µm2 pixel sizecovering Bragg angles between 10° and 21°. 2x2 binning was used to speed detector readout.Assuming ideal diffraction geometry, the instrument resolution is estimated to be 0.005 to 0.015Å for a given interplanar spacing of 0.5 to 2.5 Å, respectively. The minimum time resolutionthat can be attained in this set up without deterioration of signal to noise ratio was found to be 3s. Therefore, in early stages of transformation the time resolution was set to 3 s and at the laterstages of transformation the time resolution was increased to 34 s. The powder diffraction ringswere integrated to give 1D scans of intensity versus interplanar spacing [13, 14].

The samples after the transformation were characterized by optical microscopy, automatedhardness testing equipment and Philips XL-30FEG scanning electron microscopy. The energydispersive X-ray mapping was performed with 250 nm intervals with 20 s dwell time whileoperating at 15 kV on a polished surface.

In addition to results from these heat-treatment experiments, the current work also utilized someof the published in-situ diffraction results measured during welding from another steel [15].These measurements were performed at Stanford Synchrotron Radiation Laboratory and thetime-resolution for this experiment was 0.05s.

Results and Discussions

Analyses of Transformation KineticsThe dynamics of phase transformations from austenite to bainitic ferrite were monitored with thein situ time-resolved X-ray diffraction technique using synchrotron radiation in two samples.The crystal structure of austenite is face-centered cubic (FCC) and that of ferrite is body-centeredcubic (BCC). A series of thousands of diffraction rings from {111}FCC, {011}BCC and {002}FCC

at different time intervals were integrated into an image format as a function of time at theisothermal transformation temperature. The diffraction results from two samples aresummarized in Fig. 2. The images show changes in the diffraction patterns and lattice parameterchanges during the isothermal hold at 573 K from 10 to 30000 s. For sample 1, the image [seeFig 2a] shows only the {111}FCC and {002}FCC diffraction peaks in the early stages ofisothermal heat treatment. This diffraction evidence shows that the sample is fully austenitic onreaching 573 K. With increasing time at 573 K, the width of the {111}FCC peak increases andthe intensity distribution becomes bimodal at the point indicated by an arrow “A” in the plot.This occurs before any detectable transformation to ferrite. Ferrite eventually appears, asindicated by [see Arrow B] the faint diffracted intensity from {011}BCC. At this stage, the widthof {002}FCC diffraction peaks also increased. In sample 2, the image [see Fig. 2b] showspredominantly {111}FCC and {002}FCC diffraction peaks and a weak {011}BCC diffraction peak


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at the early stages of transformation. The widths of both {111}FCC and {002}FCC diffractionpeaks are large and each has a bimodal intensity distribution (peak “splitting”). Analysis showedthat the splitting of {111}FCC peaks occurred during cooling from high temperatures to theisothermal transformation temperature. At longer times at 573 K, the ferrite fraction increasedand the positions of the FCC diffraction peaks moved towards higher interplanar spacings. Thelattice parameter of the austenite became more uniform as the ferrite fraction increased, as shownby arrows “A” and “B” in the images.

Comparison of results in figure 2 shows subtle differences in the measurements from the samples1 and 2 before reaching the isothermal temperature, even though the samples are of the samecomposition and were subjected to similar heat-treatment. It is speculated that this differencecould be due to local differences in austenite grain structure during cooling. Further high-speedX-ray diffraction characterization during continuous cooling is needed to evaluate the possiblecauses for these differences.

The data shown in the Fig. 2 measured during isothermal treatment were further analyzed byfitting a Gaussian peak to all the individual ferrite and austenite diffraction peaks of the form.

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I = Io expd − dow

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(1).

I corresponds to the observed diffraction intensity as a function of interplanar spacing, I0 is theintensity for a given mean interplanar spacing d0 and w is given by the Gaussian peak width. Inaddition, the areas under the {111}FCC and {011}BCC peaks were also calculated. The integratedareas were converted to phase fraction by considering structure factor, multiplicity factor,Lorentz polarization and temperature factor with the standard methodology [16].

The variations of mean interplanar spacing for FCC {111} (d111) and BCC {011} (d011) planesand width of FCC {111} (w111) and BCC {011} (w011) peaks are shown in Fig. 3. In bothsamples, d111 increased with increase in ferrite fraction, as expected from the partitioning ofcarbon into the austenite. In sample 1, before the onset of the austenite to bainitic ferritetransformation, d111 slightly increased from 2.095 Å to 2.098 Å within the time period 10 to 300-s, this being accompanied by an increase in w111 from 0.008 to 0.009 Å. Although this increasewas within the estimated instrument resolution of 0.015 Å, the observed increase w111 was verysystematic. This systematic increase is puzzling given that the change occurs in the absence oftransformation. With sample 2, d111 increased slightly from 2.099 Å to 2.101 Å within the timeperiod of 10 to 100-s, as the ferrite fraction increased slightly from 0.05 to 0.07. During thisperiod, w111 remained constant at a higher value of 0.014 Å; this larger value compared withsample 1 is simply due to some ferrite forming in the sample before the transformationtemperature was reached. In conjunction with these measurements, at the early stages ofisothermal holding until 100s, temperature fluctuations were also observed in both experiments.However, these fluctuations (see Figure 6) reduced after 100s, however, the austenite diffractionpeaks showed some anomalous behavior. These unusual variations of widths of austenitediffraction peaks will be analyzed in depth later in this paper.

In sample 1, d011 systematically decreased from 2.047 Å to 2.044 Å as the isothermal holdingtime increased from 614 to 30000 s. This is indeed expected, since the ferrite initially issupersaturated with carbon, some of which then partitions into the austenite, leading to adecrease in the ferrite lattice parameter. At any given time, the ferrite lattice parameter may have


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a wide range of values as the ferrite carbon concentration within plates that have formed atdifferent times. As a result, w011 increases from 0.009 Å to 0.015 Å; this interpretation mightseem inconsistent with the observations on sample 2 (where d011 goes through a maximum), butit is important to note that in that case, w111 is much larger, possibly because due to a morenonuniform distribution of carbon in the parent austenite. For this reason, w011 from the sample2 is also larger than sample 1, due to the corresponding greater range of carbon in the ferrite.

Assuming that the lattice parameter variations can be attributed to carbon concentration, thelatter can be estimated for ferrite using d011. Using a published relationship that relates the ferritelattice parameter to alloying element concentrations [17,18], the carbon in ferrite was estimated forboth sample 1 and sample 2. The calculation technique is described below.

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d{011}BCC = aBCC 2

aBCC = 2.8664 +aFe − 0.279MC( )2 aFe + 2.496MC( ) − aFe3

3aFe2

− 0.03MSi + 0.06MMn + 0.07MNi + 0.31MMo + 0.05MCr + 0.096MV

(2)

In the above equation, Mi corresponds to the mole fraction of elements “i” in the ferrite. Sincethe mobility of substitutional atoms is very sluggish at 573 K, the mole fractions of Si, Mn, Ni,Mo, Cr, and V are made equal to their nominal concentrations in the alloy. The lattice parameterof pure iron (aFe) is 2.8664 Å. In addition, to calculate the lattice parameter at 573 K, the thermalexpansion coefficient of ferrite was derived from the diffraction data from on-heatingmeasurements and was found to be 1.3864 × 10-5 K-1. With the above equation, the range ofcarbon concentration was found to be 1.8 to 2.8 at. % (0.4 to 0.62 wt.%) for both samples duringthe isothermal transformation. This is consistent with recent observations using an atom probe[12], which revealed a range in ferrite of 0.15 to 2.27 at% (0.03 to 0.5 wt.%).

The optical microstructure and hardness variations from the same sample are shown in Fig. 4.The low magnification micrograph shows an island of untransformed region [see Fig. 4a].Similar regions were found throughout the sample and are attributed to the untransformedaustenite, which is stabilized by the partitioning of carbon from supersaturated ferrite [12]. Thesame micrograph shows that there is no significant carbon depletion due to decarburization fromthe surface. Moreover, the micrograph shows the presence of a thin layer of oxide on the surfaceof the sample. This indeed was detected by the diffraction measurements and identified aspredominantly magnetite (Fe2.9O4) and small amounts of hematite (Fe2O3). Possible overlappingof austenite and oxide peaks during analysis were also ruled out based on the measured intensityfrom the oxide peaks. A high magnification micrograph [see Fig. 4b] showed the presence ofboth martensite and bainitic microstructure. Spatial hardness [see Fig. 4c] measurements showedlarge variations in the hardness with some regions of hard spots.

Analyses of Austenite Diffraction PeaksThe variation of w111 in sample 1 prior to transformation, and the large value of w111 in sample 2are now discussed. It may not be justified to treat the {111} data as a single peak, as shown inFigure 5 but rather as the superposition of two peaks, both originating from the austenite. This isreferred to here as “peak splitting” as might occur if carbon-rich and carbon-poor regionsdevelop spontaneously. The deconvolution of the data in Figure 5 was done using a Gaussian


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shape†. Similar splitting was also observed in the {002}-austenite peaks. The intensity of thelow d111 peak decreases as ferrite develops, which would be consistent with the elimination oflow-carbon austenite which transforms first, and due to any enrichment of the austenite withcarbon partitioned from bainitic ferrite (Figure 5). The data can also be used to estimate phasefractions, as shown in Figure 6. The temperature fluctuations are seen to cause correspondingchanges in the measured lattice spacings. As stated before, the fraction of the smaller latticeparameter austenite decreased as ferrite formed.

The carbon concentrations of the two types of austenite can be estimated if it is assumed thatparameter variations are due to carbon variations. The calculation technique is described below.From the published relationship [17,18] between the austenite composition and lattice parameter atroom temperature (300 K) (aFCC), the carbon concentrations of these austenite regions can beestimated.

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d{111}FCC = aFCC 3aFCC = 3.5780 + 0.033xc + 0.00095xMn − 0.0002xNi + 0.0006xCr

+ 0.0056xAl + 0.0031xMo + 0.0018xV

(3).

In the above equation xi corresponds to the weight percent of elements “i” in the austenite. Inaddition, to calculate the lattice parameter at 573 K, an estimate of the thermal expansioncoefficient of austenite is necessary. The thermal expansion coefficient of austenite wasmeasured to be 2.5032 × 10-5 K-1 from the on-cooling diffraction data. It is important to note thatthe measured thermal expansion coefficient of austenite is higher than other low-carbon steels(1.9 × 10-5 K-1) measured using dilatometer techniques [19]. Recently, Acet et al [20] reportedthermal expansion coefficient of austenite higher than 2 × 10-5 K-1 in simple Fe-C steels. Thehigh thermal expansion coefficient in the current steels is tentatively attributed to high coolingrate and also high carbon concentrations. Using the measured thermal expansion coefficient, thelattice parameter at 573 K was calculated for both low- and high-carbon austenite regions of thesample 1. After 300 s isothermal hold, the carbon-poor austenite region corresponds to 0.62wt.% C and the carbon-rich austenite to 1.03 wt.% C. It is interesting that the ferrite carbonconcentration ranges from 0.40 to 0.62 wt.%. This may be because it is the low-carbon austenitethat transforms first, an interpretation, which would be consistent with the suggestions of Klierand Lyman [5], Entin [6] and recently by Wu et al. [11].

Other Mechanisms for Peak SplittingBefore the discussion of the mechanisms for this peak splitting, it is important to comment on theuse of simple symmetric Gaussian peak fitting in the previous section. It is important to notethat asymmetry of diffraction peaks may develop due to the presence of internal stresses anddislocation characteristics within the grain of any alloy [21]. Because the current isothermalheat-treatments were done without any mechanical deformation, the use of symmetric Gaussianpeaks is assumed to be valid. In addition, the data from sample 1 also showed the enhancementof peak splitting (or asymmetry) during isothermal hold [see Fig. 6a], which can not beexplained based on the generation of certain types of dislocations during isothermal hold. Inthis section, other possible causes of the peak splitting are discussed.

† The dynamics of peak splitting shown in Fig. 5 are shown in a movie format at the followinglocation: http://mjndeweb.ms.ornl.gov/BES/Supplement/Peak/BabuetalPaper.htm


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(1) The lattice parameter of austenite is also depends on substitutional solutes [Equation 3]. Anyvariation in substitutional solute content could in principle lead to corresponding changes in theaustenite lattice parameter. Although the alloy used had been given a homogenization heattreatment to minimize the presence of any solidification-induced chemical segregation, theremay remain residual variations, which were characterized energy dispersive X-ray peak intensitymapping. The peak intensities of Si, Mn, Cr and Fe are mapped from a local region of thesamples heat-treated at 573 K [see Fig. 7]. In these grey scale images, the maximum intensitycorresponds to white color and the zero intensity corresponds to black color. The maps shownonly random variations and do not correlate with the observed microstructure. On comparing tothe intensity of iron peaks, these random variations are not significant, and certainly not largeenough (equation 3) to cause peak splitting. Atom probe compositional analysis in the same steelafter similar heat-treatments in many different regions failed to show any change in the nominalconcentration of substitutional element concentration [12].

Notice that any form of substitutional solute segregation present in the austenite cannot in anycase explain why the austenite, during isothermal holding, first has a single lattice parameter,which splits into two peaks as a function of time.

(2) Carbon concentration gradients may develop if the carbides precipitate from the austeniteduring cooling from austenitizing temperature. However, the alloy is designed with a high siliconcontent, precisely to avoid carbides. Extensive electron microscopy and atom probe microscopyanalysis of the same steel has demonstrated the absence of carbides in the microstructure [12].

(3) One possibility is decarburization from the surface of the sample contributing to carbonvariations in the austenite. Careful optical microscopy and hardness measurements failed toshow any decarburization. Again, this cannot explain why the austenite, during low-temperatureisothermal holding following austenitisation, first has a single lattice parameter, which splits intotwo peaks as a function of time. In addition, the decarburization also will lead to peakbroadening not peak splitting.

(4) Substitutional atom might diffuse via some sort of a spinodal within the 400 s of theobserved lattice parameter fluctuations at 573 K. However, the diffusivities of substitutionalelements ranges from 1 x 10-29 to 1 x 10-31 m2s-1 in the austenite phase at 573 K compared to acarbon diffusivity of 8 x 10-19 m2s-1 [22]. The estimated diffusion distance (

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2 Dit ) forsubstitutional atoms for 400 s at 573 K in austenite is 1 x 10-14 to 1 x 10-13 m, which is less thanthe interatomic distance. In contrast, the diffusion distance for carbon atoms is expected to be 36nm. Therefore, the observed austenite diffraction peak splitting after reaching 573 K cannot beattributed to diffusion of substitutional atoms.

(5) A particle size L will give a diffraction peak width w=0.6d2/L; w111=0.01 Å corresponds toL=260 Å. While the ferrite would be expected to nucleate with a small particle size within theaustenite, there is no reason to expect such a dramatic decrease in the austenite particle size inthe early stages of transformation. An inhomogeneous stress distribution with Gaussian widthwstress will give peak width w=wstressd/G, where G=75 GPa is the shear modulus of austenite.w111=0.01 Å corresponds to wstress=360 MPa. Transformation stresses might be this large in thesmall fraction of ferrite, but not in the bulk of the austenite. However, during the formation ofplate shaped ferrite, the strains can be accommodated entirely in the austenite [23]. These strainswill not be uniform, increasing with magnitude as the plate shape is reached. Moreover, thesetwo sources of broadening would not be expected to produce a peak splitting.


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(6) A possible cause of carbon partitioning in austenite is spinodal decomposition. A solidsolution can become heterogeneous by spinodal decomposition, if the enthalpy of solution issuch that it favors the clustering of like atoms; in these circumstances, the free energy of mixingcan show two minima as a function of concentration, leading to the possibility of spinodaldecomposition at low temperatures. The molar Gibbs energy of austenite and ferrite as a functionof carbon concentration was calculated using ThermoCalc® software [24] and Thermo-Tech Irondatabase [25] [see Fig. 8]. The second derivative of Molar Gibbs energy (

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d2G dx 2 ) of austenitewith respect to carbon concentration was always positive [26], a condition inconsistent with theexistence of a spinodal. This is inconsistent with our tentative conclusion that the latticeparameter fluctuations are associated with carbon concentration variations on an unspecifiedscale, but one could argue that the thermodynamic data on which the calculations are based arenot appropriate for such low temperatures.

(7) One further possibility is the classical two electronic states model for austenite, in whichthere is co-existence of high and low molar volume states of austenite at any temperature; theapparently large thermal expansivity of austenite is because the fraction of each state istemperature dependent [27]. Unfortunately, this does not involve a time-dependence, which iswhat has been detected in the present experiments, and indeed, the phenomenon is independentof the presence of carbon.

Measurements in Other AlloysSuppose the interpretation of the synchrotron data is correct and that austenite does become non-uniform prior to transformation, it is relevant to ask whether this effect is general or specific tothe alloy studied. In this context, previously published time-resolved in-situ diffraction datafrom the Fe- 0.23 C- 1.77Al- 0.56 Mn wt.% steel, obtained during weld cooling, [15] wasreanalyzed. The analysis is presented in Figure 9. The left plot shows the intensity of austeniteand ferrite diffraction peaks measured at a time-resolution of 0.05 s using synchrotron radiation.At high temperature, only the {111}FCC austenite peak is present. As the weld cools down theaustenite lattice shrinks and at a critical time, the austenite diffraction peak splits into two peaks.The austenite peak with high 2θ (low d-spacing) and low 2θ (high d-spacing) is interpreted as theformation of low-carbon and high-carbon austenite. With continued cooling, the diffractionpeaks from low-carbon austenite decreases with a concurrent increase in ferrite {110}BCC

diffraction intensity. With continued cooling, the high-carbon austenite also transforms. Thequantitative analysis of the diffraction data is shown in right side of the Fig. 9 and shows that thetrends are consistent, that on cooling, the “low-carbon” austenite disappears first. It is possibletherefore that the observations made here are general.

ConclusionsTransformation kinetics and lattice parameters were measured during isothermal transformationof a high-carbon austenite to bainitic ferrite using time-resolved X-ray diffraction techniqueusing Synchrotron radiation. The analyses of diffraction peaks indicated splitting of austenitepeaks before the onset of ferrite transformation. This peak splitting was tentatively attributed tothe development of carbon-rich and carbon-poor regions in the austenite. The fraction of carbon-poor austenite region gradually decreased with the on-set of bainitic ferrite transformation. Atthe early stages of transformation, the diffraction data from ferrite also exhibited a large range oflattice parameters indicating possible carbon trapping. With continued isothermal holding, as the


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transformation progressed, the austenite lattice parameters became more uniform and increasedto higher value. Reanalysis of a published time-resolved X-ray diffraction data from a steel weldwith different composition showed similar austenite splitting and the disappearance of low-carbon austenite with the on-set of bainitic ferrite transformation, suggesting that thisphenomenon may be general.

AcknowledgementsResearch sponsored by the Division of Materials Sciences and Engineering, U. S. Department ofEnergy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC. The UNICAT facility atthe Advanced Photon Source (APS) is supported by the U.S. DOE under Award No. DEFG02-91ER45439, through the Frederick Seitz Materials Research Laboratory at the University ofIllinois at Urbana-Champaign, the Oak Ridge National Laboratory (U.S. DOE contract DE-AC05-00OR22725 with UT-Battelle LLC), the National Institute of Standards and Technology(U.S. Department of Commerce) and UOP LLC. The APS is supported by the U.S. DOE, BasicEnergy Sciences, Office of Science under contract No. W-31-109-ENG-38. The authors atUniversity of Cambridge are grateful to the Engineering and Physical Sciences ResearchCouncil, CORUS and The Worshipful Company of Ironmongers for supporting this research.The authors also thank Dr. E. A. Kenik for help with scanning electron microscopy EDSmapping.

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Engineers, 1944, 158, 394-422.

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11. Wu XL, Zhang XY, Kang MK, Meng XK, Yang YQ and Han D. Materials Transactions,

JIM., 1994, 35, 782.

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1281.13. Hammersley AP, Svensson SO, Hanfland M, Fitch AN and Häusermann D. High Pressure

Research, 1996, 14, 235.14. Hammersley AP., ESRF Internal Report, ESRF97HA02A, Fit2D: An Introduction and

Overview, 1997.

15. Babu SS, Elmer JW, Vitek JM, and David SA. Acta Materialia, 2002, 50, 4763.16. Cullity BD “Elements of X-ray diffraction,” Addison-Wesley Publishing Inc., Massachusetts,

1978.17. Bhadeshia HKDH, David SA, Vitek JM and Reed RW. Materials Science and Technology,

1991, 7, 686.

18. Dyson DJ and Holmes B, Journal of the Iron and Steel Institute, 1970, 208, 469.19. S. S. Babu, “Acicular ferrite and bainite in Fe-Cr-C weld deposits,” Ph.D. Thesis, University

of Cambridge, 1992.20. Acet M, Gehrmann B, Wassermann EF, Bach H, and Pepperhoff W, J. of Magnetism and

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Figure 1. Schematic illustration of experimental setup and in-situ diffractionmeasurements in a synchrotron beam line is shown.

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Figure 2. Image representations of diffraction data from two samples subjected to similarheat treatment are shown. In this image, the blue color corresponds to thebackground intensity and the maximum intensity is given by the red color. (a)Sample 1: Arrow A on {111}FCC line corresponds to onset of peak splitting;arrow B on {011}BCC correspond to the initiation of austenite to ferritetransformation; arrow C on the {002}FCC corresponds to the increase in thewidth of diffraction peak. (b) Sample 2: The blank white region in the imagecorresponds to absence of measurement due to a change in integration time. Thearrow A on {111}FCC diffraction line indicates a rapid rate of change of thediffraction peaks and arrow B on {002}FCC indicates a similar change.

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Figure 3. Results of data analysis from the diffraction data from (a) sample 1 and (b)sample 2 are summarized. The interplanar spacing of {111}FCC and {011}BCC,corresponding Gaussian width of the diffraction peaks, and the ferrite fractioncalculated based on area fraction of the {111}FCC and {011}BCC diffraction peaks.

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Figure 4. Optical micrographs showing the overall microstructure at differentmagnifications are presented. (a) Low magnification micrograph shows a largeisland of untransformed region (marked by arrow). The micrograph also showssmall amount of oxide on the surface of the sample (b) Higher magnificationmicrograph shows the presence of martensitic and bainitic microstructure withsmall blocks of untransformed region. (c) Spatial Vickers hardness variation inthe sample shows the presence of hard and soft regions.

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Figure 5. Analyses of {111}FCC diffraction peaks measured at different time intervals fromsample 1 during isothermal holding at 573 K are shown with the fitted peakswith a Gaussian peak shape. (a) The diffraction peaks from 0 second shows theonset of peak splitting. Diffraction peaks at (b) 102, (c) 201 and (d) 302 secondsinto isothermal hold at 573 K showing the onset and development of peaksplitting. The diffraction data obtained after the ferrite transformation at (e)1000 and (f) 4000 seconds show the reduction of low-carbon austenite fraction.The data from sample 2 at (g) 0-s into isothermal hold shows the presence ofpeak splitting as well as (h) reduction of low-carbon austenite peak intensityafter 100-s hold.

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Figure 6. (a) Analysis of {111}FCC diffraction splitting at early stages of isothermal hold at573 K before the onset of ferrite transformation from sample 1. Measuredtemperature, d-spacing of low- and high-carbon austenite and phase fractions ofthe of low- and high-carbon austenite as a function of time. (b) Similar analysison data from sample 2 shows the reduction of low-carbon austenite fraction withincrease in ferrite fraction.

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Figure 7. Results of energy dispersive X-ray spectrum analysis from the sample after theheat treatment at 573 K shows no large compositional gradients with referenceto substitutional alloying additions Cr, Si and Mn. The gray scale imagecontrast ranges to minimum of zero and maximum of intensity ranges quoted inthe maps.

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Figure 8. Comparison of the measured diffracted intensities from low- and high-carbonaustenite at time 0- and 302-seconds with reference to calculated molar Gibbsfree energy of the austenite and ferrite as a function of carbon concentration.The nominal carbon concentration of the alloy is also shown. The plots also showthe second derivative of the Gibbs free energy of austenite as a function ofcarbon concentration in the austenite.

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Figure 9. In-situ X-ray diffraction measurements taken at 0.05-second intervals duringrapid cooling of a Fe-C-Al-Mn steel weld and the analyses of the data: The leftside of the figure is the image representation of measured diffraction intensity(white background, black high intensity) during rapid cooling from the liquidstate. The image is overlaid with the peak position of two austenite peaks as wellas the ferrite peak position. The right side of the figure shows the calculatedarea fraction from peak area as a function of weld cooling time. During theinitial stages (from 2.0 to 2.6 seconds) of measurements, the weld cools rapidlyand may have averaging effect. The rate of change of temperature can bevisualized by the change in slope of the 2θ with time.

In-situ Observations of Lattice Parameter Fluctuations in ......S. S. Babu Formerly at Metals and...

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